Question

Simultaneous Equations: Solve y - 2x = 3 and x^2 + y^2 = 18

Answer 1

y - 2x = 3
x^2 + y^2 = 18

y = 3 + 2x

x^2 + (3 + 2x)^2 = 18

x^2 + (3 + 2x)(3 + 2x) = 18

x^2 + 9 + 12x + 4x^2 = 18

5x^2 + 12x + 9 = 18

5x^2 + 12x - 9 = 0
                 
5x2 - 3x + 15x - 9

(x + 3)(5x - 3) = 0

X = -3, 3/5

y = 3 + 2x

y = 3 + 2(-3)         y = 3 + 2(3/5)
y = -3                    y = 4.2

(x,y) = (-3,-3), (0.6,4.2)